## Acta Mathematica

### The tempered spectrum of a real spherical space

#### Abstract

Let $G/H$ be a unimodular real spherical space which is either absolutely spherical, i.e. the real form of a complex spherical space, or of wave-front type. It is shown that every tempered representation for $G/H$ embeds into a twisted discrete series for a boundary degeneration of $G/H$. If $G/H$ is of wave-front type it follows that the tempered representation is parabolically induced by a twisted discrete series representation for a real spherical space formed by a Levi subgroup.

#### Note

The second author was supported by ERC Advanced Investigators Grant HARG 268105.

#### Article information

Source
Acta Math., Volume 218, Number 2 (2017), 319-383.

Dates
Revised: 12 August 2016
First available in Project Euclid: 31 January 2018

https://projecteuclid.org/euclid.acta/1517426686

Digital Object Identifier
doi:10.4310/ACTA.2017.v218.n2.a3

Mathematical Reviews number (MathSciNet)
MR3733102

Zentralblatt MATH identifier
1381.22010

#### Citation

Knop, Friedrich; Krötz, Bernhard; Schlichtkrull, Henrik. The tempered spectrum of a real spherical space. Acta Math. 218 (2017), no. 2, 319--383. doi:10.4310/ACTA.2017.v218.n2.a3. https://projecteuclid.org/euclid.acta/1517426686